I am aware that the issue of non-proportional hazards during survival analysis has been examined from a statistical point of view in the past and relevant literature exists. However, I was wondering if there is literature (or experts opinion) regarding the biological reasons (nature of disease?) or study design (follow-up imbalance?) that may explain the presence of non-proportional hazards.
If you get the assumptions wrong the probability statements will be incorrect. See the book in the link.
https://www.amazon.com/Survival-Event-History-Analysis-Keiding/dp/0470058064/ref=sr_1_fkmrnull_2?keywords=andersen+survival+analysis&qid=1551911268&s=books&sr=1-2-fkmrnull
As for the biology you should know it if you see it. the assumption check for Cox regression tells you. Best, David Booth
Some biological sources of non proportionality would be saturation effects of a drug (ie no more effect abover a certain dose), toxic effects above a certain dose, threshold effect (no effect until a certain dose reached).
biases in follow up would be a patient source,
uncontrolled covariates would be another source.
In the CLARICOR team we have discussed this question. The main clue here is that early diers are different from late diers; or else no interesting multivariate survival analyses would exist.
Also: Suppose a biomarker M gives a clear picture of the prognosis 6 mths hence. Another marker (or genotype) P is a long-term mortality marker. M and P are assessed on subjects' 60th birthday, say, and a multivariate regression analysis is undertaken. If they are correlated, (M, P) will predict a hazard dominated by M for some months but then dominated by P.
[NOTE: Leigh's first remark refers to non-linearity of the hazard measure ("vertical failure of Cox assumption," curves not equidistant), not to proportional hazard curves ("longitudinal failure," curves not congruent).]
Yours, JH
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